On the interpolation by discrete splines with equidistant nodes. (English) Zbl 0941.41002

Pevnyi, Alexander B.; Zheludev, Valery A.

J. Approximation Theory 102, No. 2, 286-301 (2000).

In this paper the authors develop the theory of non-periodic discrete splines of power growth. Such splines are relevant for the purposes of digital signal processing. Discrete \(B\)-splines are introduced as linear combinations of shifts of the \(B\)-splines. Here the authors present a solution of the problem of discrete spline cardinal interpolation of the sequences of power growth and prove that the solution is unique within the class of discrete splines of a given order.

Reviewer: Ganesh Datta Dikshit (Auckland)

MSC:

41A05	Interpolation in approximation theory
41A15	Spline approximation

Keywords:

wavelets; digital signal processing; discrete \(B\)-splines; non-periodic discrete splines; cardinal interpolation

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